Given that a > 0, f (x) = - X3 + ax is a monotone decreasing function in [1, + ∞), then the maximum value of a is () A. 1B. 2C. 3D. 4

Given that a > 0, f (x) = - X3 + ax is a monotone decreasing function in [1, + ∞), then the maximum value of a is () A. 1B. 2C. 3D. 4

∵ f (x) = - X3 + ax, ∵ f ′ (x) = a-3x2, ∵ function f (x) = ax-x3 monotonically decreases in the interval [1, + ∞), ∵ f ′ (x) = a-3x2 ≤ 0 is constant in the interval [1, + ∞), ∵ a ≤ 3x2 is constant in the interval [1, + ∞), ∵ a ≤ 3